Information on Result #700704

Linear OA(317, 88, F3, 6) (dual of [88, 71, 7]-code), using construction XX applied to C1 = C({0,1,2,53}), C2 = C([0,4]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C({0,1,2,4,53}) based on
  1. linear OA(313, 80, F3, 5) (dual of [80, 67, 6]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,53}, and minimum distance d ≥ |{−1,0,1,2,3}|+1 = 6 (BCH-bound) [i]
  2. linear OA(313, 80, F3, 5) (dual of [80, 67, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
  3. linear OA(317, 80, F3, 6) (dual of [80, 63, 7]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,53}, and minimum distance d ≥ |{−1,0,…,4}|+1 = 7 (BCH-bound) [i]
  4. linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
  5. linear OA(30, 4, F3, 0) (dual of [4, 4, 1]-code), using
  6. linear OA(30, 4, F3, 0) (dual of [4, 4, 1]-code) (see above)

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

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Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(317, 87, F3, 2, 6) (dual of [(87, 2), 157, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(317, 87, F3, 3, 6) (dual of [(87, 3), 244, 7]-NRT-code) [i]
3Linear OOA(317, 87, F3, 4, 6) (dual of [(87, 4), 331, 7]-NRT-code) [i]
4Linear OOA(317, 87, F3, 5, 6) (dual of [(87, 5), 418, 7]-NRT-code) [i]